Davis-Wielandt-Berezin radius inequalities of Reproducing kernel Hilbert space operators

Abstract

Several upper and lower bounds of the Davis-Wielandt-Berezin radius of bounded linear operators defined on a reproducing kernel Hilbert space are given. Further, an inequality involving the Berezin number and the Davis-Wielandt-Berezin radius for the sum of two bounded linear operators is obtained, namely, if $A$ and $B$ are reproducing kernel Hilbert space operators, then $$\eta (A+B)\le \eta (A)+\eta (B)+\text{ber}(A^{\ast }B+B^{\ast }A),$$ where $\eta (\cdot )$ and $\text{ber}(\cdot )$ are the Davis-Wielandt-Berezin radius and the Berezin number, respectively.

17 pages